506 A. Yaughan — Problem of a Cooling Earth, 



Eeade's theory, as epitomised by him in the May Number of the 

 same Journal. In a short reply, contributed by Mr. Eeade to the 

 September Number, he shows so clearly that he has totally mis- 

 understood the physical reasoning upon which my theory is based, 

 that some rejoinder is absolutely demanded. 



In criticising my theory, he asks : " How then could the under- 

 layers, by shrinking, exert such a huge pressure on the interior as 

 to actuallj' compress the materials of the earth into a smaller volume ?" 

 and, a few lines further on, he proposes that we should "work out 

 the decrease of volume which would result from a given contraction 

 of a shell of steel, 30 miles thick, acting on a sphere of the size and 

 composition of our earth." 



Did I rely upon actual decrease of volume due to pressure, my 

 theory would, of course, be absurdly untenable ; but my reasoning 

 is based upon the transference of material from beneath a surface of 

 great pressure to below a surface upon which the pressure is much 

 less. This I have so frequently reiterated in my paper that I could 

 quote from almost any page ; perhaps the following extract, taken 

 from my first paper, will suffice : " The underlying material will be, 

 so to speak, squeezed out, and this will cause a real transfer from 

 under the sinking area to beneath the surrounding regions." 



To my criticism of his own theory Mr. Eeade has not replied, but 

 he has, however, objected to my attempt to show that the reasoning 

 he employs is hardly sufficient to disprove the old contraction 

 theory. Mr. Eeade takes exception to a calculation, based upon his 

 own figures, as to the elevation which could be produced from an 

 outer shell too large, by a certain amount, for the interior sphere, 

 I took a special case, and supposed the outer shell to be drawn out 

 over the interior sphere, somewhat in the shape of a balloon, so as 

 to produce over a certain large area a vast hollow cone-shaped 

 elevation. I cannot understand how the very simple calculation 

 necessary can be called in question, and I can only suppose that 

 Mr. Eeade has assumed that any elevation must be solid. If, how- 

 ever, we accept the theory of elevation by the folding due to lateral 

 pressure, it is very difficult to see how all vacuities could be avoided, 

 and yet the known dips of anticlines produced. It is, consequently, 

 necessary in considering any elevation, which is not actually a 

 maximum, to assume that elevation to be hollow. 



The last point raised by Mr. Eeade is one of much greater 

 interest, and it directly introduces the main object of this paper. 

 Stated in its simplest form, the physical problem is : — What would 

 be the behaviour of a contracting shell closely fitted round a sphere 

 unalterable in volume ? (This is, in reality, the same as supposing 

 such a shell to surround a less rapidly contracting interior.) Here 

 we can easily distinguish two cases. 



First, the shell may be contracting unequally at points whose 

 distance from the centre is the same. This is the actual problem 

 in the case of the earth, as I have shown in a former paper ; and 

 the results I believe to follow may be briefly recapitulated. 



Any contracting area must attempt to become smaller, and this 



